At present, M-ary QAM (M-QAM) is used to provide high-speed data transfer in conjunction with a number of mobile data communication applications. However, a primary drawback of M-QAM is its computational complexity. One prior art approach for addressing this shortcoming involves the use of square M-QAM constellations, such as 16QAM, 64QAM, and 256QAM. Square constellations may be conceptualized as including two independent q-ary amplitude shift keying (q -ASK) modulation signals as real and imaginary parts (in-phase and quadrature-phase components of a modulated carrier), where q=√{square root over (M)}.
For example, a 16-QAM signal includes two independent real and imaginary 4-ASK signals. A q-ASK signal takes on values selected from the set
      {                  ±                  1          2                    ,              ±                  3          2                    ,      …      ⁢                          ,              ±                              q            -            1                    2                      }    .Representing a square-constellation M-QAM signal in q-ASK format is usually preferred because the complexity of processing a q-ASK signal is significantly less than that of processing a general M-QAM signal.
A received M-QAM signal (rk) may be represented by the following expression:rk=A*dk+nk;  Equation (1)where A is the signal amplitude; dk represents a set of data symbols encoded onto a transmitted M-QAM or q-ASK signal; and nk represents noise. While for M-QAM signals, dk and nk are complex quantities, for q-ASK signals they are both purely real.
In order to demodulate M-QAM and q-ASK signals, it is necessary to determine the values of one or more signal parameters at the receiver, such as amplitude, noise power, and signal-to-noise ratio (SNR). Even in the case of a q-ASK signal representation, which provides enhanced computational simplicity relative to M-QAM representation, existing techniques for estimating these signal parameters are inefficient and computationally complex.
An improved technique for estimating signal parameters at the receiver is needed to provide efficient demodulation of M-QAM and Q-ASK signals.